Question

A charge ‘q' is uniformly distributed on a ring of radius ‘a'. a sphere of an equal radius is placed such that the centre of sphere is on the periphery of the ring. the flux of the electric field through the surfaces of the sphere will be

Answer 1

A charge q is distributed uniformly on a ring of radius R.A sphere of equal radius R is constructed with its centre on circumference of ring.Find electric flux through surface of sphere.Explanation is must.....

Answer 2

let point of intersection of ring & sphere are P,Q ...let center of ring is O & center of sphere is O¹ ...

OO¹ bisects PQ in two equal parts , if S is the point of intersection of OO¹ & PQ then

in triangle right angled POS

PO = R , OS = R/2 so angle POS = θ

using trigonometry , cosθ = OS/PS = 1/2

θ = π/3

total angle substended by arc is 2π/3...this is the arc of ring which lies inside sphere & substends

2π/3 angle at the center of ring...

 

 

for 2π radian charge  = q

for unit radian = q/2π

for 2π/3 radian q1 = (q/2π)(2π/3) = q/3

total flux through sphere = total charge enclosed/ε₀= q/3ε₀

this is the required flux